EQ2EMu/EQ2/source/depends/boost_1_72_0/libs/math/test/condition_number_test.cpp

//  (C) Copyright Nick Thompson, 2019
//  Use, modification and distribution are subject to the
//  Boost Software License, Version 1.0. (See accompanying file
//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

#define BOOST_TEST_MODULE condition_number_test

#include <cmath>
#include <limits>
#include <iostream>
#include <boost/math/constants/constants.hpp>
#include <boost/math/special_functions/lambert_w.hpp>
#include <boost/test/included/unit_test.hpp>
#include <boost/multiprecision/cpp_bin_float.hpp>
#include <boost/math/tools/condition_numbers.hpp>

using std::abs;
using boost::math::constants::half;
using boost::math::constants::ln_two;
using boost::multiprecision::cpp_bin_float_50;
using boost::math::tools::summation_condition_number;
using boost::math::tools::evaluation_condition_number;

template<class Real>
void test_summation_condition_number()
{
    Real tol = 1000*std::numeric_limits<float>::epsilon();
    auto cond = summation_condition_number<Real>();
    // I've checked that the condition number increases with max_n,
    // and that the computed sum gets more accurate with increasing max_n.
    // But the CI system would die with more terms.
    Real max_n = 10000;
    for (Real n = 1; n < max_n; n += 2)
    {
        cond += 1/n;
        cond -= 1/(n+1);
    }

    BOOST_CHECK_CLOSE_FRACTION(cond.sum(), ln_two<Real>(), tol);
    BOOST_TEST(cond() > 14);
}

template<class Real>
void test_exponential_sum()
{
    using std::exp;
    using std::abs;
    Real eps = std::numeric_limits<float>::epsilon();
    for (Real x = -20; x <= -1; x += 0.5)
    {
        auto cond = summation_condition_number<Real>(1);
        size_t n = 1;
        Real term = x;
        while(n++ < 1000)
        {
            cond += term;
            term *= (x/n);
        }
        BOOST_CHECK_CLOSE_FRACTION(exp(x), cond.sum(), eps*cond());
        BOOST_CHECK_CLOSE_FRACTION(exp(2*abs(x)), cond(), eps*cond());
    }
}



template<class Real>
void test_evaluation_condition_number()
{
    using std::abs;
    using std::log;
    using std::sqrt;
    using std::exp;
    using std::sin;
    using std::tan;
    Real tol = sqrt(std::numeric_limits<Real>::epsilon());

    auto f1 = [](auto x) { return log(x); };
    for (Real x = 1.125; x < 8; x += 0.125)
    {
        Real cond = evaluation_condition_number(f1, x);
        BOOST_CHECK_CLOSE_FRACTION(cond, 1/log(x), tol);
    }

    auto f2 = [](auto x) { return exp(x); };
    for (Real x = 1.125; x < 8; x += 0.125)
    {
        Real cond = evaluation_condition_number(f2, x);
        BOOST_CHECK_CLOSE_FRACTION(cond, x, tol);
    }

    auto f3 = [](auto x) { return sin(x); };
    for (Real x = 1.125; x < 8; x += 0.125)
    {
        Real cond = evaluation_condition_number(f3, x);
        BOOST_CHECK_CLOSE_FRACTION(cond, abs(x/tan(x)), tol);
    }

    // Test a function which right differentiable:
    using boost::math::constants::e;
    auto f4 = [](Real x) { return boost::math::lambert_w0(x); };
    Real cond = evaluation_condition_number(f4, -1/e<Real>());
    if (std::is_same_v<Real, float>)
    {
        BOOST_CHECK_GE(cond, 30);
    }
    else
    {
        BOOST_CHECK_GE(cond, 4900);
    }
}


BOOST_AUTO_TEST_CASE(numerical_differentiation_test)
{
    test_summation_condition_number<float>();
    test_summation_condition_number<cpp_bin_float_50>();
    test_evaluation_condition_number<float>();
    test_evaluation_condition_number<double>();
    test_evaluation_condition_number<long double>();
    test_evaluation_condition_number<cpp_bin_float_50>();
    test_exponential_sum<double>();
}